Certainly not.
What do you think that would fix? It would just make for an infuriating first 5 games for new users and give them an unrealistic picture of this site.
I've got a mentee right now who's a ? and a better, more dedicated player then most who have posted in this thread.
Worse case scenario: the dreaded 'noob' enters your game and deadbeats, oh no! What shall we do??? Each time his turn comes we will have to wait for it too pass?!?! How dare he HOLD UP MY GAME!

Not like we don't have unlimited other ones to play (if your a free member, you have no room to complain).
Alienating new users by segregating them to play games with each other is not the key to site longevity and growth, nor to having a 'better' player-base. A site like this will ALWAYS have a high turnover rate, like all online gaming sites. Many people will sign up, decide it's not suited to their tastes and never return.
You wanna make this site better? Instead of bitching/complaining about the new guys, take a few minutes of your precious time and help one out by showing him the ropes.